The article Simultaneous Optimization of Mechanical Properties of Steel by Maximizing Exponential Desirability Functions (K. J. Kim and D. K. J. Lin, Journal of the

The article €œSimultaneous Optimization of Mechanical Properties of Steel by Maximizing Exponential Desirability Functions€ (K. J. Kim and D. K. J. Lin, Journal of the Royal Statistical Society Series C, Applied Statistics, 2000: 311€“325) presents measurements on 72 steel plates. The following MINITAB output presents the results of a study to determine the relationship between yield strength (in kg/mm²), and the proportion of carbon, manganese, and silicon, each measured in percent. The model fit is Yield strength = β₀+ β₁Carbon + β₂Manganese + β₃Silicon + ε

Of the following, which is the best next step in the analysis? Explain your reasoning.

i. Add interaction terms Carbon · Manganese and Manganese · Silicon to try to find more variables to put into the model.

ii. Add the interaction term Carbon · Silicon to try to find another variable to put into the model.

iii. Nothing needs to be done. This model is fine.

iv. Drop Carbon and Silicon, and then perform an F test.

v. Drop Manganese, and then perform an F test.

The regression equation is Yield Strength - 24.677 19.402 Carbon + 14.720 Manganese + 70.720 Silicon Predictor StDev 5.8589 28.455 5.6237 45.675 Coef 24.677 -19.402 14.720 70.720 4.21 -0.68 2.62 0.000 0.498 Constant Carbon Manganese Silicon 0.011 0.126 1.55